Computational Methods and Function Theory 9 (2009), No. 1, 127--143
Copyright Heldermann Verlag 2009
Mohamed M. S. Nasser
mms_nasser@hotmail.com , Ibb University, Faculty of Science, Department of Mathematics, P.O.Box 70270, Ibb, Yemen.
A boundary integral method is presented for constructing approximations to the mapping functions of bounded multiply connected regions to the standard canonical slits domains given by Nehari [11]. The method is based on expressing the mapping function in terms of the solution of a Riemann-Hilbert problem which can be solved by a uniquely solvable boundary integral equation with the generalized Neumann kernel. Three numerical examples are presented to show the effectiveness of the present method.
[11] Z. Nehari, Conformal Mapping, Dover Publications, Inc, New York, 1952.
Keywords: Numerical conformal mapping, multiply connected regions, generalized Neumann kernel, Riemann-Hilbert problem.
MSC 2000: Primary 30C30; Secondary 30E25, 45B05.
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